Dynamic Factor Graphs for time series modeling
This is my thesis research project under
Prof. Yann LeCun's supervision, published in
Lecture Notes in Artificial Intelligence and presented at
ECML-PKDD 2009.
A DFG includes factors modeling joint probabilities between hidden and observed variables, and factors modeling dynamical constraints on hidden variables. The DFG assigns a scalar energy to each configuration of hidden and observed variables. A gradient-based inference procedure finds the minimum-energy state sequence for a given observation sequence. Because the factors are designed to ensure a constant partition function, they can be trained by minimizing the expected energy over training sequences with respect to the factors' parameters. These alternated inference and parameter updates can be seen as a deterministic gradient-based EM-like procedure.Using smoothing regularizers, DFGs have been shown to reconstruct chaotic attractors and to separate a mixture of independent oscillatory sources perfectly. DFGs outperformed the best known algorithm on the CATS competition benchmark for time series prediction. DFGs also successfully reconstruct missing motion capture data. For more details, download the article, or follow the video lecture at ECML-PKDD 2009, with corresponding slides.